Standard form of the polynomial is [tex]x^{7}-2 x^{6}-3 x^{5}+x^{2}+\sqrt{2} x+4[/tex].
Degree of the polynomial is 7.
Solution:
Given polynomial:
[tex]x^{7}-3 x^{5}+\sqrt{2} x+x^{2}-2 x^{6}+4[/tex]
To write this polynomial in standard form:
[tex]x^{7}-3 x^{5}+\sqrt{2} x+x^{2}-2 x^{6}+4[/tex]
Standard form of the polynomial is writing x from highest power to lowest power.
Therefore, standard form of the polynomial is
[tex]x^{7}-2 x^{6}-3 x^{5}+x^{2}+\sqrt{2} x+4[/tex]
Degree of the polynomial:
The highest power of x in the polynomial is the degree of the polynomial.
Here, the highest power is 7.
Hence the degree of the polynomial is 7.
